离散数学英文试题A参考答案及评分标准
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西南大学课程考核
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《离散数学》课程试题 【A 】卷参考答案和评分标准
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6. Solution
(10 points )
7. Solution (1) Suppose G has x vertices of degree 1. 3∙3 + 1∙2 + x ∙ 1 = 2((x + 4) - 1) x = 5 G has 9 vertices. (10 points ) (2)
(5 points )
8. Proof Suppose that (p → q ) ∧ (p → r ) is true. We want to show that p → (q ∧ r ) is true, which means that we want to show that q ∧ r is true whenever p is true. If p is true, since we know that both p → q and p → r are true from our assumption, we can conclude that q is true and that r is true. Therefore q ∧ r is true, as desired.
Conversely, suppose that p → (q ∧ r ) is true. We need to show that p → q is true and that p → r is true, which means that if p is true, then so are q and r . But this follows from p → (q ∧ r ).